Stable operation of aircraft engine compressions is constrained by rotating surge. In this paper, an approximate nonlinear surge margin model of aircraft engine compression system by using equilibrium manifold is pres...Stable operation of aircraft engine compressions is constrained by rotating surge. In this paper, an approximate nonlinear surge margin model of aircraft engine compression system by using equilibrium manifold is presented. Firstly, this paper gives an overview of the current state of modeling aerodynamic flow instabilities in engine compressors. Secondly, the expansion form of equilibrium manifold is introduced, and the choosing scheduling variable method is discussed. Then, this paper also gives the identification procedure of modeling the approximate nonlinear model. Finally, the modeling and simulations with high pressure （liP） compressor surge margin of the aircraft engine show that this real-time model has the same accuracy with the thermody- namic model, but has simpler structure and shorter computation time.展开更多
In this paper, we present a mathematical model that describes tumor-normal cells inter- action dynamics focusing on role of drugs in treatment of brain tumors. The goal is to predict distribution and necessary quantit...In this paper, we present a mathematical model that describes tumor-normal cells inter- action dynamics focusing on role of drugs in treatment of brain tumors. The goal is to predict distribution and necessary quantity of drugs delivered in drug-therapy by using optimal control framework. The model describes interactions of tumor and normal cells using a system of reactions^diffusion equations involving the drug concentration, tumor cells and normal tissues. The control estimates simultaneously blood perfusion rate, reabsorption rate of drug and drug dosage administered, which affect the effects of brain tumor chemotherapy. First, we develop mathematical framework which mod- els the competition between tumor and normal cells under chemotherapy constraints. Then, existence, uniqueness and regularity of solution of state equations are proved as well as stability results. Afterwards, optimal control problems are formulated in order to minimize the drug delivery and tumor cell burden in different situations. We show existence and uniqueness of optimal solution, and we derive necessary conditions for optimality. Finally, to solve numerically optimal control and optimization problems, we propose and investigate an adjoint multiple-relaxation-time lattice Boltzmann method for a general nonlinear coupled anisotropic convection-diffusion system （which includes the developed model for brain tumor targeted drug delivery system）.展开更多
基金National Natural Science Foundation of China (61104146)Innovation Plan of Aero Engine Complex System Safety by the Ministry of Education Chang Jiang Scholars of China (IRT0905)
文摘Stable operation of aircraft engine compressions is constrained by rotating surge. In this paper, an approximate nonlinear surge margin model of aircraft engine compression system by using equilibrium manifold is presented. Firstly, this paper gives an overview of the current state of modeling aerodynamic flow instabilities in engine compressors. Secondly, the expansion form of equilibrium manifold is introduced, and the choosing scheduling variable method is discussed. Then, this paper also gives the identification procedure of modeling the approximate nonlinear model. Finally, the modeling and simulations with high pressure （liP） compressor surge margin of the aircraft engine show that this real-time model has the same accuracy with the thermody- namic model, but has simpler structure and shorter computation time.
文摘In this paper, we present a mathematical model that describes tumor-normal cells inter- action dynamics focusing on role of drugs in treatment of brain tumors. The goal is to predict distribution and necessary quantity of drugs delivered in drug-therapy by using optimal control framework. The model describes interactions of tumor and normal cells using a system of reactions^diffusion equations involving the drug concentration, tumor cells and normal tissues. The control estimates simultaneously blood perfusion rate, reabsorption rate of drug and drug dosage administered, which affect the effects of brain tumor chemotherapy. First, we develop mathematical framework which mod- els the competition between tumor and normal cells under chemotherapy constraints. Then, existence, uniqueness and regularity of solution of state equations are proved as well as stability results. Afterwards, optimal control problems are formulated in order to minimize the drug delivery and tumor cell burden in different situations. We show existence and uniqueness of optimal solution, and we derive necessary conditions for optimality. Finally, to solve numerically optimal control and optimization problems, we propose and investigate an adjoint multiple-relaxation-time lattice Boltzmann method for a general nonlinear coupled anisotropic convection-diffusion system （which includes the developed model for brain tumor targeted drug delivery system）.
